Which is the worst opening for white?
I'd argue that 1. f3 is the worst. You don't develop a piece, you prevent your kingside knight from reaching it's best square, and you weaken your kingside. The three you listed are wasteful moves to be sure, but 1. f3 wastes a tempo with flare!
f3 or f4, because when I play these I usually lose
I agree with Probaddie 1.f3 is the worst and h3 a close second since it weakens your kingside pawn structure.
As for Two_Dogs, I use 1.f4 and win regularly but there are a lot of traps to avoid.
Well the sodium opening is pretty bad tho..
I vote for 1. f3 (Gedult's Opening), for the reasons at the above linked thread.
It's rated next to last in popularity on 365 chess:
NAMES OF ALL THE FIRST OPENING MOVES(in order of descending frequency, per 365chess)1. e4 - King's Pawn Game , King's Pawn Opening 1. d4 - Queen's Pawn Game 1. Nf3 - Zukertort Opening, Reti Opening 1. c4 - English Opening1. g3 - Hungarian Opening, Benko's Opening , King's Fianchetto Opening 1. f4 - Bird Opening, Bird's Opening 1. b3 - Larsen's Opening , Nimzo-Larsen Attack, Nimzovich-Larsen Attack 1. Nc3 - Van Geet Opening, Dunst Opening 1. b4 - Polish Opening, Sokolsky Opening , The Orangutan 1. e3 - Van't Kruijs Opening 1. d3 - Mieses Opening 1. a3 - Anderssen Opening1. c3 - Saragossa Opening 1. g4 - Grob Opening, Grob's Attack , Spike Opening , Kolibri's Opening 1. h3 - Clemenz Opening 1. Nh3 - Amar Opening , Paris Opening , Drunken Knight Opening , or Ammonia Opening 1. h4 - Kadas Opening, Desprez Opening 1. a4 - Ware Opening, Meadow Hay Opening 1. f3 - Gedult's Opening, Barnes Opening 1. Na3 - Sodium Attack, Durkin Opening 
REFERENCEShttp://www.chess.com/explorer/ http://en.wikipedia.org/wiki/Desprez_Opening http://en.wikipedia.org/wiki/Durkin_Opening http://en.wikipedia.org/wiki/Dunst_Opening http://en.wikipedia.org/wiki/Barnes_Opening (1-27-15) http://en.wikipedia.org/wiki/Sokolsky_Opening http://en.wikipedia.org/wiki/Grob%27s_Attack (1-25-15) http://en.wikipedia.org/wiki/Ware_Opening http://en.wikipedia.org/wiki/Benko%27s_Opening (1-25-15) http://en.wikipedia.org/wiki/King%27s_Pawn_Game http://en.wikipedia.org/wiki/Queen%27s_Pawn_Game http://en.wikibooks.org/wiki/Chess_Opening_Theory/1._b4 (1-25-15) http://en.wikipedia.org/wiki/Larsen%27s_Opening (1-25-15) http://www.365chess.com/opening.php (1-25-15) http://en.wikipedia.org/wiki/Van_%27t_Kruijs_Opening (1-25-15) http://en.wikipedia.org/wiki/Mieses_Opening (1-25-15) http://en.wikipedia.org/wiki/Saragossa_Opening (1-25-15) http://en.wikipedia.org/wiki/Amar_Opening (1-25-15) http://en.wikipedia.org/wiki/Clemenz_Opening (1-25-15)
e3 isn't bad if you end up transposing with d4 or f4 afterwards. The other two moves are just punts that offer Black to open the game and play a tempo down but with a minor rook-pawn move already made.
White can get away with a lame move in the opening. Black is down a tempo and can't fiddle around so much.